Fermat's Last Theorem (redirected from Fermet's Last Theorem)

Fermat's last theorem

Statement that there are no natural numbers x, y, and z such that xⁿ + yⁿ = zⁿ, in which n is a natural number greater than 2. About this, Pierre de Fermat wrote in 1637 in his copy of Diophantus's Arithmetica, “I have discovered a truly remarkable proof but this margin is too small to contain it.” Although the theorem was subsequently shown to be true for many specific values of n, leading to important mathematical advances in the process, the difficulty of the problem soon convinced mathematicians that Fermat never had a valid proof. In 1995 the British mathematician Andrew Wiles (b. 1953) and his former student Richard Taylor (b. 1962) published a complete proof, finally solving one of the most famous of all mathematical problems.

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Fermat's last theorem [fer′mäz ¦last ′thir·əm]

(mathematics)

The proposition, proven in 1995, that there are no positive integer solutions of the equationxⁿ+yⁿ=zⁿforn≥ 3.

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Fermat’s Last Theorem 

(or Fermat’s great theorem), the assertion of P. Fermat that the Diophantine equation xⁿ + yⁿ = zⁿ, where n is an integer greater than 2, has no solution in positive integers. The theorem has been proved for a number of values of n, but no proof has been given for the general case.

Despite the simplicity of the formulation of Fermat’s last theorem, its complete proof apparently requires the development of new and profound methods in the theory of Diophantine equations. An unhealthy interest in the proof of the theorem among nonspecialists in mathematics was stimulated at one time by a large international prize, which was withdrawn at the end of World War I.

REFERENCES

Dickson, L. E. History of the Theory of Numbers, vols. 1–3. New York, 1934.
Landau, E. Aus der algebraischen Zahlentheorie und über die Fermatsche Vermutung. (Vorlesungen über Zahlentheorie, vol. 3.) Leipzig, 1927.